Swans midfielder Bersant Celina followed up his stunning strike against former club Manchester City by opening his account for Kosovo on Thursday night.
The 22-year-old edged his country ahead in a friendly against Denmark in Pristina, which ended 2-2 after the visitors equalised in additional time.
Celina has scored goals in 38 appearances for the Swans this season following his summer switch from the Premier League champions.
Oli McBurnie, meanwhile, led the line as Scotland went down to a shock 3-0 defeat in their opening Euro 2020 qualifier against Kazakhstan.
The striker, who has missed the Swans' last few games through illness, featured for 61 minutes before he was replaced by Johnny Russell.